Question

Use square roots to solve the equation x2 = –64 over the complex numbers. Select any solutions that apply.
A. 8i
B. –8
C. –8i2
D. –8i

Answer 1

Answer:

Options A and D are correct

Step-by-step explanation:

Here, we want to find the square root of the negative number;

x^2 = -64

x^2 = 64 * -1

x= √64 * √-1

Mathematically we can write the √-1 as i

X = √64 * i

Square root of 64 is plus or minus 8

so x = -8i or 8i

Answer 2

The solutions of an equation are the true values of the equation.

The expression that represents the solution(s) of $\mathbf{8i}$ is $\mathbf{-8i}$

The equation is given as:

$\mathbf{x^2 = -64}$

Take square roots of both sides

$\mathbf{x = \pm\sqrt{-64}}$

Expand

$\mathbf{x = \pm(\sqrt{64} \times \sqrt{-1})}$

$\mathbf{x = \pm(8 \times \sqrt{-1})}$

In complex numbers,

$\mathbf{ \sqrt{-1} = i}$

So, we have:

$\mathbf{x = \pm(8 \times i)}$

$\mathbf{x = \pm8i}$

Split

$\mathbf{x = 8i\ or -8i}$

So, the expression that represents the solution(s) of $\mathbf{8i}$ is $\mathbf{-8i}$

Read more about expressions at:

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